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Zero Value of a Polynomial

We know that the value of a polynomial differs according to the value of the variable in it. For example, if p(x) is a polynomial with variable x and we put different values of x in p(x), then we will get different values of p(x). In some cases, the value of p(x) can be the same for two or more values of x. Also, in a few cases, the value of p(x) can be zero. 

The values of the variable at which a polynomial becomes zero are called zeroes of the polynomial. These values are very special and useful to us. Zeroes of polynomials are used in:

  • Solving problems related to [[mn:glossary]]motion[[/mn:glossary]]

  • Solving problems related to [[mn:glossary]]path[[/mn:glossary]] or [[mn:glossary]]locus[[/mn:glossary]] of a [[mn:glossary]]point[[/mn:glossary]] or geometric figure

  • Making graphs for economic [[mn:glossary]]data[[/mn:glossary]]

In this lesson, we will learn to check whether or not the given values are zeroes of the given polynomials. We will also learn to find the zeroes of different polynomials.


Zeroes or Roots of a Polynomial 

If the value of a polynomial p(x) at x = a is zero, then a is said to be the zero or root of the polynomial p(x). Let us consider the polynomial p(x) = x2 − 5x + 6 and check its values at
x = 1, 2 ….


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